Under this definition, if \(Q\)  is totally symmetric, then \(p\)  is the additive identity, \(-x = px\) , and the
addition thus defined is associative if and only if \(Q\)  is medial
(see the beautiful exercise 1.11 in [1]}, which inspired the author's investigation into these objects).
This addition enjoys the useful property that
the sum of any two rational points on an elliptic curve \(\mathcal {C}\)  is itself a rational point on \(\mathcal {C}\) .
